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The application of hybrid nanoparticles rather than nanoparticles is one of the greatest critical tasks for enhancing heat transfer. Therefore, the purpose of this article is to analyze the flow and heat transfer resulting from an exponentially decreased sheet of hybrid nanoparticles. The magnetite (Fe 3 O 4 ) and copper (Cu) nanoparticle are suspended in ethylene glycol (EG) to form Fe 3 O 4 –Cu/EG hybrid nanofluid. The PDEs governing equations of the issue have been solved after conversion to ODEs by using suitable similarity transformations. The resultant system is then solved numerically by the aid of Runge–Kutta–Fehlberg method (RKF45) with the shooting technique. The most important results of this study are the effect of different variable parameters such as permeability of porous media, the stretching/shrinking parameter, heat generation/absorption effect, slip, and nanoparticle volume fraction on the velocity, temperature profiles, skin friction coefficient, and local Nusselt number. Furthermore, the impacts of radiation, magnetohydrodynamic (MHD), suction/injection parameter, and Prandtl number are also taken into consideration. The influence of important physical parameters is discussed through graphs and tables. It is found that the increase of Fe 3 O 4  nanoparticle concentration enhances the heat transfer rate of the hybrid nanofluid in a shrinkable case, the opposite happens in a stretchable state.

Thermal conductivity variation and heat generation effects on magneto-hybrid nanofluid flow in a porous medium with slip condition